Examples update for v0.1 (#206)

* modify examples/problems
* modify tutorials

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it>
Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>

examples/run_wave.py

@@ -0,0 +1,64 @@
+""" Run PINA on Burgers equation. """
+
+import argparse
+import torch
+from torch.nn import Softplus
+
+from pina import LabelTensor
+from pina.model import FeedForward
+from pina.solvers import PINN
+from pina.plotter import Plotter
+from pina.trainer import Trainer
+from problems.wave import Wave
+
+class HardMLP(torch.nn.Module):
+
+    def __init__(self, **kwargs):
+        super().__init__()
+
+        self.layers = FeedForward(**kwargs)
+        
+    # here in the foward we implement the hard constraints
+    def forward(self, x):
+        hard_space = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))
+        hard_t = torch.sin(torch.pi*x.extract(['x'])) * torch.sin(torch.pi*x.extract(['y'])) * torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*x.extract(['t']))
+        return hard_space * self.layers(x) * x.extract(['t']) + hard_t
+
+if __name__ == "__main__":
+
+    parser = argparse.ArgumentParser(description="Run PINA")
+    parser.add_argument("--load", help="directory to save or load file", type=str)
+    parser.add_argument("--epochs", help="extra features", type=int, default=1000)
+    args = parser.parse_args()
+
+
+    # create problem and discretise domain
+    wave_problem = Wave()
+    wave_problem.discretise_domain(1000, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])
+
+    # create model
+    model = HardMLP(
+        layers=[40, 40, 40],
+        output_dimensions=len(wave_problem.output_variables),
+        input_dimensions=len(wave_problem.input_variables),
+        func=Softplus
+    )
+
+    # create solver
+    pinn = PINN(
+        problem=wave_problem,
+        model=model,
+        optimizer_kwargs={'lr' : 0.006}
+    )
+
+    # create trainer
+    directory = 'pina.wave'
+    trainer = Trainer(solver=pinn, accelerator='cpu', max_epochs=args.epochs, default_root_dir=directory)
+
+
+    if args.load:
+        pinn = PINN.load_from_checkpoint(checkpoint_path=args.load, problem=wave_problem, model=model)
+        plotter = Plotter()
+        plotter.plot(pinn)
+    else:
+        trainer.train()